Linear robust models for international logistics and inventory problems under uncertainty

Globalisation presents business organisations with some special challenges that they have never met before; they have to manage their activities in the ambit of global supply chain networks. Traditional managerial approaches, techniques and principles are no longer effective in dealing with these challenges. This article examines logistics and inventory problems in a supply chain operating in two countries where decisions have to be made with uncertain customer information. There are some differentials between two countries in terms of vehicle operation cost and capacity, labour cost, warehousing cost, etc. This article proposes three different types of robust models to integrate logistics and inventory processes between the two counties for coping with uncertain customer shipment information and the risk it entails. The first model is called the robust optimisation model with solution robustness, which provides an integrated logistics and inventory solution that is less sensitive to realisations of stochastic parameters. The second type of model is called the robust optimisation model with model robustness allowing late delivery (if it is profitable). The third type of model is called the robust optimisation model with trade-off between solution robustness and model robustness. It provides a direct way to measure the trade-off between risk and cost during the international transportation process. A series of experiments demonstrate that the proposed robust models can provide effective integrated logistics and inventory systems between two countries, which is important in today's highly competitive and dynamic business environment